The South Korean opened the scoring early in the second half to help Spurs on their way to an emphatic Champions League victory.
Vertonghen delivered an expert assist before he converted a cross from Serge Aurier to make it 2-0.
And substitute Fernando Llorente made it three to give Tottenham some comfort going into the second leg in Germany.
And Son was delighted with the performance of his team-mates even without the injured Harry Kane and Dele Alli.
He said: “Jan Vertonghen is technically unbelievable and can play in any position. I am very happy for him, he deserved it.
“One goal and an assist! The timing of the first goal was very important, the cross was unreal, I didn’t have to do anything, just touch the ball.
“It’s not finished, we have to focus on the second game too. Harry or Dele are very important for us but we have players who can come in and do well.
“We showed that, Fernando came on too and scored an important goal.”
Vertonghen was pleased with how Tottenham reacted to being under pressure in the first 45 minutes.
And the Belgian opened up on the special moment of netting in a Champions League game at Wembley.
He explained: “They looked very strong and had the better of the game but in the second half we were able to turn it around.
“They dropped off a bit then that early goal in the second half helped. We had the confidence to keep going.
“It was [my first goal] since the first game this season and I had to wait for goal line technology then so I was happy that I could just go [to celebrate this time]!
“It was at Wembley too in the Champions League so it was special. It was one of those nights.
“We were able to keep them quiet in the second half and they weren’t able to be clinical. The game changed in the second half definitely.”
Tottenham now have an emphatic lead to take into the second leg on March 5.
And Manchester United legend Rio Ferdinand was very impressed with Spurs.
He said: “It was phenomenal. Mauricio Pochettino has to take huge credit for the way he tweaked the full-backs.
“The individual performances from Eriksen, Vertonghen, Sissoko and Son…
“In the first half Dortmund looked like the team top of the Bundesliga but the contrast to the second half was huge.”
Tottenham return to action against Burnley in the Premier League on Saturday, February 23.